Technicolor (physics) - Early Technicolor

Early Technicolor

Technicolor is the name given to the theory of electroweak symmetry breaking by new strong gauge-interactions whose characteristic energy scale Λ_TC is the weak scale itself, Λ_TC ≅ F_EW ≡ 246 GeV. The guiding principle of technicolor is "naturalness": basic physical phenomena should not require fine-tuning of the parameters in the Lagrangian that describes them. What constitutes fine-tuning is to some extent a subjective matter, but a theory with elementary scalar particles typically is very finely tuned (unless it is supersymmetric). The quadratic divergence in the scalar's mass requires adjustments of a part in, where M_bare is the cutoff of the theory, the energy scale at which the theory changes in some essential way. In the standard electroweak model with M_bare ∼ 1015 GeV (the grand-unification mass scale), and with the Higgs boson mass M_physical = 100–500 GeV, the mass is tuned to at least a part in 1025.

By contrast, a natural theory of electroweak symmetry breaking is an asymptotically-free gauge theory with fermions as the only matter fields. The technicolor gauge group G_TC is often assumed to be SU(N_TC). Based on analogy with quantum chromodynamics (QCD), it is assumed that there are one or more doublets of massless Dirac "technifermions" transforming vectorially under the same complex representation of G_TC, T_iL,R = (U_i,D_i)_L,R, i = 1,2, …, N_f/2. Thus, there is a chiral symmetry of these fermions, e.g., SU(N_f)_L ⊗ SU(N_f)_R, if they all transform according the same complex representation of G_TC. Continuing the analogy with QCD, the running gauge coupling α_TC(μ) triggers spontaneous chiral symmetry breaking, the technifermions acquire a dynamical mass, and a number of massless Goldstone bosons result. If the technifermions transform under _EW as left-handed doublets and right-handed singlets, three linear combinations of these Goldstone bosons couple to three of the electroweak gauge currents.

In 1973 Jackiw and Johnson and Cornwall and Norton studied the possibility that a (non-vectorial) gauge interaction of fermions can break itself; i.e., is strong enough to form a Goldstone boson coupled to the gauge current. Using Abelian gauge models, they showed that, if such a Goldstone boson is formed, it is "eaten" by the Higgs mechanism, becoming the longitudinal component of the now massive gauge boson. Technically, the polarization function Π(p2) appearing in the gauge boson propagator, Δ_μν = (p_μ p_ν/p2 - g_μν)/ develops a pole at p2 = 0 with residue F2, the square of the Goldstone boson's decay constant, and the gauge boson acquires mass M ≅ g F. In 1973, Weinstein showed that composite Goldstone bosons whose constituent fermions transform in the “standard” way under SU(2) ⊗ U(1) generate the weak boson masses

This standard-model relation is achieved with elementary Higgs bosons in electroweak doublets; it is verified experimentally to better than 1%. Here, g and g′ are SU(2) and U(1) gauge couplings and tanθ_W = g′/g defines the weak mixing angle.

The important idea of a new strong gauge interaction of massless fermions at the electroweak scale F_EW driving the spontaneous breakdown of its global chiral symmetry, of which an SU(2) ⊗ U(1) subgroup is weakly gauged, was first proposed in 1979 by S. Weinberg and L. Susskind. This "technicolor" mechanism is natural in that no fine-tuning of parameters is necessary.